The Electron  a Uniton Dynamical Subsystem in the Cosmic
Uniton FieldThe Variable Extension of the Electron  calculated cosmologically
The Mass of the Universe Determined by Atomic Physical Quantities
Electrical and Gravitational Forces, Caused by Uniton Pushing Forces

By Louis Nielsen, Senior Physics Master, Herlufsholm

Introduction: What is an electron?

The electron was discovered as an 'independent' particle in 1897 by the
British physicist Joseph John Thomson (1856-1940) after extensive
experiments with cathode rays. (J.J.Thomson: 'Cathode Rays', Philosophical
Magazine, vol. 44, (1897)). This year, one hundred years after its
discovery, there is no total understanding of this particle, although
it is part of all matter. To regard the electron as a 'fixed', limited
ball with a definite radius, mass and an inner 'mystical' electrical
charge, responsible for a so called electrical force effect, does not
give a satisfactory deeper understanding of what an electron really is.
The wave quantum mechanical description of an electron does neither
give a physical, logical understanding of what an electron is. What
is then an electron? In the following I shall set forth new theoretical
considerations of the subsystem we call an electron. I assume that
electrons are dynamical subsystems in the Universe under constant
development.
Electrons can be considered as Bose-Einstein condensates consisting of
unitons situated in the cosmic
uniton field. The de Broglie wavelength of a uniton is equal to the
extension of the Universe.
The present new cosmological dependent theory is based
on my quantum cosmology with the main title: Holistic Quantum
Cosmology with Decreasing Gravity.
(see this).
A consequence of this theory is that gravity in the Universe is
constantly decreasing. A mechanical/physical explanation of gravity
and its decrease, I have explained in another article with the
title: Uniton Mechanical Explanation of Gravity
(see this).
As the Universe expands and gravity decreases, this
will cause that physical geometrical extensions of different subsystems,
such as f.i. an electron, also expand gradually as the Universe expands.
In the following I shall deduct an equation, showing how the extension
of an electron varies with the expansion of the Universe. The equation
shows the intimate connection between microcosmos and macrocosmos. It allows
me also to calculate the mass of the Universe by means of known atomic
physical quantities! In other words: the discovered equation shows that an
electron grows in extension as the Universe gets older!

I shall also show a physical-mechanical connection between what we call
respectively 'gravitational' forces and 'electrical' forces. Fundamentally
these forces are a result of mechanical pushing effects  of different
intensity  caused by the ubiquituous UNITONS, my name for the physical
smallest matter/energy quanta in the Universe. This connection between
gravity and electricity, which physicists for centuries have tried to
find, I believe thus to have discovered, and I shall explain this
discovery in the following.

A consequence of my Holistic Quantum Cosmology with Decreasing
Gravity (see this)
is the existence of a cosmic uniton field (also
called uniton space) consisting of the physical smallest 'matter/energy
quanta' in the Universe. These elementary quanta, with a geometrical
extension equal to the elementary length, I call unitons. They
are present all over the Universe and move with the speed of light.
'Matter' are regions in the cosmic uniton field where the density of
unitons is highly increased (viz. higher number of unitons per unit of
volume). An electron can be considered as a 'condensate', consisting of
about 1037 unitons. An electron is not a passive
particle, but on the contrary an active uniton dynamical
subsystem in the cosmic uniton field! An electron in dynamical
balance emits and absorbs the same number of unitons per unit
of time. An electron out of dynamical balance will 'seek' towards
balance, by either to emit more unitons than it absorbs or absorb
more unitons than it emits. An electron, absorbing a surplus of
unitons, is 'lifted' to a higher energy level. As unitons are discrete
quanta, they can only be emitted or absorbed in whole numbers, which
means that the energy is also increased in discrete quanta.
The electron can thus be found in different discrete states of
energy (quantum states). Surplus emission of unitons (relatively
to uniton absorption) can be identical to an emitted photon. As I have
mentioned in another section, a photon can be imagined to be
'oscillation quanta' in the cosmic uniton field or perhaps
clusters of a certain huge number of unitons, corresponding
to the energy of a certain photon. If a photon is an 'oscillation
quantum' in the cosmic uniton field, then these oscillations are
caused by accelerating electrons. These two 'photon possibilities'
can perhaps give the physical reply to the question why 'photons' in
certain cases are registered as waves and in other cases as particles.
An analog process can be observed in normal matter, through which
'sound oscillation quanta', called phonons' can be transmitted.
Phonons have many similarities to photons in their physical behavior and
can mathematically be described in exactly the same way as photons!

If an electron has a surplus absorption of unitons, this may correspond
to the absorption of a photon.

The effect of forces between two electrons.

Let us consider two electrons in rest in the cosmic uniton field.
According to known physics, it is assumed that two different
natural forces are active between the electrons, namely partly so called
attracting gravitational forces, partly repulsive electrical
forces. The gravitational forces are calculated by Newton's gravitational
law, and the electrical forces by Coulomb's electrostatic force law. The
mathematical form of these two force laws is completely identical, which
in itself is thought-provoking. The electrical force on each electron,
however, is 4.16 · 1042 times greater than the
gravitational force. According to my quantum cosmological theory,
this figure is valid only in our epoch of the evolution of the Universe,
and the number, designated N in my theory, is very important to the
whole theory.

Let us pose the following question: Is it possible that both the
electrical and the gravitational forces  and for that matter, all
forces  can be related to and explained by mechanical uniton
forces? My opinion is yes! I shall motivate my opinion in the
following.

If the gravitational and electrical forces between two electrons shall
be explained with mechanical uniton forces, the sum of uniton forces,
corresponding to what we call electrical forces, must be about
1042 times higher than the sum of the uniton forces
corresponding to the gravitational force.

The magnitude of the gravitational force Fg on an electron
is given by Newton's gravitational law:

(1)

where G is Newton's gravitational 'constant' me the mass of
the electron and r the distance between the two electrons in question.

The magnitude of the electrostatic force Fe on each
electron can be calculated by Coulomb's electrostatic force law:

(2)

where kc is Coulomb's constant and e is the electric charge
of the electron. The ratio between Fe and Fg
defines the number N.

The ratio between the mass densities of the electron and the
Universe.

Let us calculate the ratio between the density of an electron,
, and the average density of the Universe,
. This is given by:

(3)

where re is the 'extension' of an electron, M0
is the total mass of the Universe and R its present extension. For the
mass and the extension of the universe I use the values I have
calculated in my quantum cosmological theory. For the 'extension'
of the electron, I use a measured value (re,mes ~
10-18 m, see f.i.
http://www.iop.org/Physics/Electron/Exhibition/section1/
properties.html). The used values are subject to some uncertainty,
and this will of cause appear again in the calculated ratio in equation
(3). When the known (but uncertain) values are inserted in (3) we get:

(4)

which, as seen, very interestingly is a value near to the number N.
This can not be accidental, there must be a deeper connection!
With more accurate values for the known numbers I am sure that this
ratio will be equal to the number N. In order to proceed with my
theoretical calculations, I shall assume that this is the case.
The consequences must show if I am right Thus we have:

(5)

The expression in equation (5) gives us an utterly important and
interesting connection between mostly all the physical quantities, defined
by man in order to describe and understand the Universe, of which we
are ourselves a part. The ratio (5) can also be expressed as the
ratio between the uniton density in an electron, nu,e and
the uniton density in the universe, nu,cos, viz. the
following is also valid:

(6)

In the following sections, I shall use the connections given by (5) and (6).

The extension of an electron.

Equation (5) gives a connection between the extension of an electron,
its mass, electrical charge, Newton's gravitational 'constant', the
actual extension of the Universe and its mass. Isolating re
we get:

(7)

Using the earlier given values for R, M0 and N we get for the
extension of the electron:

(8)

a value very near to the experimental found. Again it must be stressed
that there are uncertainties on the values of R and M0. The
accuracy of these values is determined by the accuracy, by which it is
possible to measure the relative variation of Newton's gravitational
'constant'.The expression in (7) gives a connection between the
extension of an electron and the extension of the Universe and its mass.
That such a holistic context exists was already proposed by the English
astro physicist Arthur Stanley Eddington (1882-1944) in 1923.
In his once so famous textbook 'The Mathematical Theory of Relativity',
Cambridge University Press (1923), Eddington writes:

"radius of an electron in any direction = a numerical constant times the
radius of curvature of space-time in that direction."

Equation (7) gives such a context. It should be noted, however, that
Eddington before 1929 used the static model of the Universe, which
Willem de Sitter (1872-1934) and Einstein worked out, based on Einstein's
General Theory of Relativity. Extragalactic systems were for the first time
discovered by Edwin Hubble (1889-1953) in 1923. It was also
Hubble who discovered the spectral redshift of light from the galaxies
in 1929, a phenomenon which has later been interpreted as a universal
doppler effect, caused by a general expansion of the Universe. Taking
the expansion of the Universe in consideration, as I do, means that the
connection between the extension of an electron and cosmological quantities
become more complicated than originally imagined by Eddington.

The extension of a proton

An interesting question is: Is equation (7) also valid for a proton (and maybe
for other so called "elementary particles")? Let us use it on a proton with
the mass mp = 1.67 · 1027 kg. For the extension
rp we get:

The mass of the Universe determined by atomic physical
constants and the gravitational 'constant'.

Instead of expressing the extension of the electron by cosmological
quantities, such as the mass of the Universe and its extension, we can
on the other hand deduct a connection between the mass of the Universe,
M0, and physical quantities, of which the value is well known,
maybe just except the extension of the electron. Converting equation
(8) gives:

(9)

where I have used the following cosmologic basical equation from my
holistic quantum cosmology
(see this)
for the connection between the extension of the Universe, R, and elementary
length r0, which on the other hand is determined by Planck's
constant, the velocity of light and the mass of the Universe:

(10)

Equation (9) can be written in the following way:

(11)

where mx gives the mass of a particle, probably important?
As the mass of the Universe is determined by the mass and extension of
the electron, it would seem to show that it is the mass of a so called
W-particle, which 'appears' at interactive effects, where so called
weak nuclear forces are involved. The measured value of the mass of
the W-particle is very near to the mass which I have called mx,
and is of the magnitude of 10-25 kg, where the mass of the
W-particle is measured to about 1.4 · 10-25 kg.

The growing electron.

From equation (5) we see that as R, and thereby also G, is changing,
some of the other elements in the equation must also change, when the
Universe expands. To be in agreement with the assumption I have done
in my cosmological theory, f.i. that the mass and electrical charge
of an electron are constant, it follows that the extension of an
electron will change during time. The equation I deduct shows that
electrons increase in extension. In earlier epochs of the development
of the Universe their extension was smaller, which of course is quite
logical, for how would there otherwise be space for them in a Universe
having smaller and smaller volume, when we go back in time?
Let us deduct a differential equation for the relative variation of the
extension of an electron. Equation (5) can be rewritten as:

(12)

By differentiation of re relative to time (marked by a dot),
we get after some calculation:

(13)

The connection between the relative variation of the extension of the
Universe and the relative variation
of Newton's gravitational 'constant' has been
deducted in my cosmological theory, and is given by:

(14)

Using this expression in (13) we get:

(15)

The connection between and the actual age of the
Universe, T, is given by:

(16)

which inserted in (15) gives a connection between the relative variation
of the extension of an electron and the actual age of the Universe.
We get:

(17)

If we wish to get a direct connection between the extension of an electron
and the age of the Universe, we can integrate (17) and get:

(18)

where k is an integration constant. The value of this constant we can
determine from the values we know for our epoch. Using values as I
have used earlier in this article, we get:

(19)

Equation (19) of course is only valid from the 'moment' when electrons
were created. The extension of an electron can never have been smaller
than elementary length r0 = 10-102 meter.
By equation (18) we can calculate the extension of an electron at
different ages of the Universe. Let us as an example calculate what
the extension of an electron was when the Universe was half a billion
years old, viz. when T = 1.6 · 1016 second. From (18)
we get:

(20)

From (20) we see that an electron about 10 billion years ago had an
extension about ten times smaller than an electron in our epoch! We
can study the processes going on with such electrons by observing
very distant objects in the Universe, such as quasars. That the
quasars emit very large energies from very small regions can possibly
be understood by a.o. the present theory.

Electrical and gravitational forces reduced to uniton
pushing forces.

By means of the connections found above it can be shown that what we call
'electrical' forces can be related to what we call 'gravitational'
forces. The latter forces can be explained physically-mechanically as
collision forces between unitons. This I have explained in another article.
Electrical forces can thus also be related to uniton pushing forces,
however in a much more intense form.
Let us convert equation (5) as follows:

(21)

From (21) we see that we can express what we have introduced and called
'electric charge' by purely mechanical and geometrical quantities, namely
mass densities and Newton's gravitational 'constant', which appears as a
coupling parameter.
We now convert Coulomb's electrostatical force law, (2), by using (21)
and we get:

(22)

which is a purely mechanical force law. The explanation, why two
electrons repulse each other with forces N times higher than the
forces by which they are pushed together, is that the mass density
of an electron  or the uniton density  is N times higher than the
average overall density of the Universe!
That electrons repulse each other is due to the fact that electrons
emit and absorb unitons.
The above has shown that electrical and gravitational forces have a
common cause. It will also be possible to refer the so called strong
and weak nuclear forces to the same fundamental, cosmological level.

The constancy of electrical forces.

The expression in (22) gives the magnitude of what we have called the
'electrical' force on an electron, caused by the presence of another
electron. You may ask if this 'electrical' force has had the same
magnitude, also in earlier epochs of the Universe. If Fe
has had the same value through the evolution of the Universe, then
the value of the quantity given in equation (23) must be constant through
the evolution of the Universe.

(23)

where index T gives the value of the inserted elements at a random
cosmical 'moment', later than the moment of creation of electrons.
Converting (23) we get:

(24)

In (24) G0 is the value of Newton's gravitational 'constant'
inside the first cosmic time quantum interval of the 'birth' of the
Universe. The value of G0 can be calculated very accurately,
as it is determined by:

(25)

We see that the expression in (23) is constant and equal to G0.
This indicates that the forces active between electrons, and which we
call electric forces, have not changed during the evolution of the
Universe, whereas the gravitational forces are constantly decreasing!
The mechanical cause for the decrease of gravity is the expansion of
the Universe, and thereby a macroscopical dilution of the cosmic uniton
field. Going back in the evolution of the Universe, the magnitude of
gravitational forces get nearer and nearer to the magnitude of the
electrical forces!